Final answer:
To simplify sin²(x)sec²(x)-sin²(x), we can use the identity sin²(x)=1-cos²(x) to simplify the expression to 1 - cos²(x).
Step-by-step explanation:
To simplify the expression sin²(x)sec²(x)-sin²(x), we can rewrite sec²(x) as 1/cos²(x). So, the expression becomes sin²(x)*(1/cos²(x))-sin²(x).
Next, we can combine the two terms by finding a common denominator. The common denominator for sin²(x)*(1/cos²(x)) and sin²(x) is cos²(x).
Using the common denominator, we get (sin²(x)*(1/cos²(x))-sin²(x))*(cos²(x)/cos²(x)).
Simplifying further, we have (sin²(x)-sin²(x)*cos²(x))/cos²(x).
Finally, we can use the identity sin²(x)=1-cos²(x) to simplify the expression to (1-cos²(x)-sin²(x)*cos²(x))/cos²(x). This can be further simplified to 1/cos²(x) - cos²(x)/cos²(x).
The simplified expression is 1/cos²(x) - 1 = 1 - cos²(x).